4 (x^(3)-9 x^(2)+6 x-6)=0

asked by guest
on Nov 25, 2024 at 6:55 am



You asked:

Solve the equation \(4 \cdot \left({x}^{3} - 9 {x}^{2} + 6 x - 6\right) = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= 3 + 2 \sqrt[3]{\frac{21}{8} + \frac{7 \sqrt{2}}{8}} + \frac{7}{2 \sqrt[3]{\frac{21}{8} + \frac{7 \sqrt{2}}{8}}} \approx 8.368715\\x &= - \sqrt[3]{\frac{7 \sqrt{2}}{8} + \frac{21}{8}} - \frac{7}{4 \sqrt[3]{\frac{7 \sqrt{2}}{8} + \frac{21}{8}}} + 3 + i \left(- \frac{7 \sqrt{3}}{4 \sqrt[3]{\frac{7 \sqrt{2}}{8} + \frac{21}{8}}} + \sqrt{3} \sqrt[3]{\frac{7 \sqrt{2}}{8} + \frac{21}{8}}\right) \approx 0.31564249 + 0.78570081 i\\x &= - \sqrt[3]{\frac{7 \sqrt{2}}{8} + \frac{21}{8}} - \frac{7}{4 \sqrt[3]{\frac{7 \sqrt{2}}{8} + \frac{21}{8}}} + 3 + i \left(- \sqrt{3} \sqrt[3]{\frac{7 \sqrt{2}}{8} + \frac{21}{8}} + \frac{7 \sqrt{3}}{4 \sqrt[3]{\frac{7 \sqrt{2}}{8} + \frac{21}{8}}}\right) \approx 0.31564249 -0.78570081 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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